from builtins import range
import numpy as np
from random import shuffle
from past.builtins import xrange

def softmax_loss_naive(W, X, y, reg):
    """
    Softmax loss function, naive implementation (with loops)

    Inputs have dimension D, there are C classes, and we operate on minibatches
    of N examples.

    Inputs:
    - W: A numpy array of shape (D, C) containing weights.
    - X: A numpy array of shape (N, D) containing a minibatch of data.
    - y: A numpy array of shape (N,) containing training labels; y[i] = c means
      that X[i] has label c, where 0 <= c < C.
    - reg: (float) regularization strength

    Returns a tuple of:
    - loss as single float
    - gradient with respect to weights W; an array of same shape as W
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)

    #############################################################################
    # TODO: Compute the softmax loss and its gradient using explicit loops.     #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    num_train, dim = X.shape
    classes = W.shape[1]
    scores = X.dot(W)
    
    sta_scores = scores - np.max(scores, axis = 1, keepdims = True) #Numerical Stability
    exp_scores = np.exp(sta_scores)
    final_scores = exp_scores/np.sum(exp_scores, axis = 1, keepdims = True)
  
    for i in range(num_train):
        loss -= np.log(final_scores[i,y[i]])
  
    loss /= num_train
    loss += reg*np.sum(np.square(W))
  
    for i in range(num_train):
        for d in range(dim):
            for c in range(classes):
                dW[d, c] += (final_scores[i, c]*X[i, d])
                if c == y[i]:
                    dW[d, c] -= X[i, d]
          
    dW /= num_train
    dW += 2*reg*W

    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW


def softmax_loss_vectorized(W, X, y, reg):
    """
    Softmax loss function, vectorized version.

    Inputs and outputs are the same as softmax_loss_naive.
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)

    #############################################################################
    # TODO: Compute the softmax loss and its gradient using no explicit loops.  #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    num_train, dim = X.shape
    classes = W.shape[1]
    scores = X.dot(W)
    
    sta_scores = scores - np.max(scores, axis = 1, keepdims = True) #Numerical Stability
    exp_scores = np.exp(sta_scores)
    final_scores = exp_scores/np.sum(exp_scores, axis = 1, keepdims = True)
    loss = -np.sum(np.log(final_scores[np.arange(num_train), y]))/num_train
    loss += reg*np.sum(np.square(W))
  
    mask = final_scores.copy()
    mask[np.arange(num_train), y] -= 1
    dW = X.T.dot(mask)/num_train
    dW += 2*reg*W

    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW
